一维周期介质中行波波包的双尺度级数展开
Two-scale series expansions for travelling wave packets in one-dimensional periodic media
摘要：
从波动方程的材料属性，周期性变化的介质，我们研究了一个系统的递归关系，描述传播的波包，振荡的微观尺度（即长度的顺序的周期的介质）和缓慢变化的宏观尺度（即长度，包含大量的周期）。由此产生的方程包含一个版本的几何光学和周期性介质的整体能量传输描述。我们说明了发达的渐近理论使用的例子，通过一个周期性的安排，具有高度对比的弹性模量的两种材料的点脉冲传播。
英文摘要：
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order of the period of the medium) and vary slowly on the macroscale (i.e. on lengths that contain a large number of periods). The resulting equations contain a version of the geometric optics and the overall energy transport description for periodic media. We illustrate the developed asymptotic theory using the example of a point pulse propagating through a periodic arrangement of two materials with highly contrasting elastic moduli.
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